Modulus of dentability in $L¹ + L^{∞}$

• Autorzy: Adam Bohonos , Ryszard Płuciennik
• Języki publikacji: EN

Abstrakty

EN

We introduce the notion of the modulus of dentability defined for any point of the unit sphere S(X) of a Banach space X. We calculate effectively this modulus for denting points of the unit ball of the classical interpolation space $L¹ + L^{∞}.$ Moreover, a criterion for denting points of the unit ball in this space is given. We also show that none of denting points of the unit ball of $L¹ + L^{∞}$ is a LUR-point. Consequently, the set of LUR-points of the unit ball of $L¹ + L^{∞}$ is empty.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 79
• Numer: 1
• Strony: 39-51

Daty

wydano

2008

Twórcy

autor

Adam Bohonos

• Institute of Mathematics, Szczecin University of Technology, Al. Piastów 48/49, 70-310 Szczecin, Poland

autor

Ryszard Płuciennik

• Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

Identyfikatory

DOI

10.4064/bc79-0-2